Find the coordinate of point p (rounded to the nearest tenth) that lies 2/3 of the way on the directed line segment xy, where point x is (-2, 5) and point y is (4, 9)

  (2, 7.7)

Step-by-step explanation:

The point P that divides XY into segments such that ...

  XP : PY = 2 : 1

will be the weighted average of X and Y:

  P = (2Y +1X)/(2+1)

  = (2(4, 9) +1(-2, 5))/3 = (6/3, 23/3) = (2, 7 2/3)

  P ≈ (2, 7.7)

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2